“We’re face-to-face with our old foe: the combinatorial explosion. Therefore we do what we always have to do in life: compromise. We make simplifying assumptions that whittle the number of probabilities we have to estimate down to something manageable. A very simple and popular assumption is that all the effects are independent given the cause. This means that, for example, having a fever doesn’t change how likely you are to also have a cough, if we already know you have the flu. Mathematically, this is saying that P(fever, cough | flu) is just P(fever | flu) × P(cough | flu). Lo and behold: each of these is easy to estimate from a small number of observations. In fact, we did it for fever in the previous section, and it would be no different for cough or any other symptom. The number of observations we need no longer goes up exponentially with the number of symptoms; in fact, it doesn’t go up at all.”